Maths puzzle

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Across
  1. 3. Q are not closed under____
  2. 4. a rational number and its additive inverse are ___in their sign
  3. 5. numbers are also called rational numbers
  4. 8. a*b belongs to Q is ___property
  5. 9. a+b =b+a is ___property
  6. 11. p/q form,p&q are Z
  7. 12. multiplicative inverse of one
  8. 13. is the additive identity for Q
Down
  1. 1. the multiplicative inverse of Q is its
  2. 2. ax0=____
  3. 4. is the multiplicative identity for Q
  4. 6. division by one
  5. 7. ax(bxc)=(axb)xc is ___ property
  6. 10. division by zero